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Results tagged with special-functions
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user 8928
Questions on the special mathematical functions implemented in Mathematica.
5
votes
1
answer
195
views
An identity involving the Weierstrass ℘-function
One of the most well-known identities involving $\wp$ is
$$\wp'^2=4 \wp^3-g_2 \wp-g_3. $$
However, when I run the command
WeierstrassPPrime[z, {g2, g3}]^2 - (4 WeierstrassP[z, {g2, g3}]^3 -
g2 Weie …
- 1,088
0
votes
1
answer
200
views
The value of $\sqrt{\frac{\pi }{2}} C(1)$
I'm going through question 5 here, where they ask to approximate the integral
$$I=\int_0^a \cos(t^2) \mathrm{d}t $$ with $a=\sqrt{\pi/2}$. This integral can be expressed using Fresnel integrals as
…
- 1,088
2
votes
1
answer
206
views
Simplifying elliptic functions
I am working with (long) elliptic functions, which are rational functions in WeierstrassP and WeierstrassPPrime. As expressed in my previous question, Mathematica isn't aware of the fact that
Weiers …
- 1,088
8
votes
1
answer
488
views
Using NDSolve on the Painlevé equations
In an earlier question of mine, I was looking for a way to handle certain kinds of singularities (poles) when using NDSolve. Michael E2's answer, which relied on projective geometry was the most upvot …
- 1,088